Slight compositional variation-induced structural disorder-to-order transition enables fast Na+ storage in layered transition metal oxides

The omnipresent Na+/vacancy orderings change substantially with the composition that inevitably actuate the ionic diffusion in rechargeable batteries. Therefore, it may hold the key to the electrode design with high rate capability. Herein, the influence of Na+/vacancy ordering on Na+ mobility is demonstrated firstly through a comparative investigation in P2-Na2/3Ni1/3Mn2/3O2 and P2-Na2/3Ni0.3Mn0.7O2. The large zigzag Na+/vacancy intralayer ordering is found to accelerate Na+ migration in P2-type Na2/3Ni1/3Mn2/3O2. By theoretical simulations, it is revealed that the Na+ ordering enables the P2-type Na2/3Ni1/3Mn2/3O2 with higher diffusivities and lower activation energies of 200 meV with respect to the P3 one. The quantifying diffusional analysis further prove that the higher probability of the concerted Na+ ionic diffusion occurs in P2-type Na2/3Ni1/3Mn2/3O2 due to the appropriate ratio of high energy ordered Na ions (Naf) occupation. As a result, the interplay between the Na+/vacancy ordering and Na+ kinetic is well understood in P2-type layered cathodes.


Supplementary Figures
. Refined X-ray powder diffraction pattern for (a) P2-Na2/3Ni1/3Mn2/3O2 and (b) P2-Na2/3Ni0.3Mn0.7O2. wherein the experimental (black circles) and calculated (red solid line), the Bragg reflection peaks (purple and magenta solid ticks) and the difference curve (blue line) are shown, respectively. The green ball represents Naf and the yellow ball stands for Nae. Figure S2. (a) Simulated XRD patterns of P2-type layered oxides with three different inplane Na + -ion/vacancy ordering (large zigzag, honeycomb and chain type). (b) A magnified view of XRD patterns between 20-38°, where the d-spacings correspond to the average distances between the adjacent intralayer sodium ions in the in-plane Na + -ion/vacancy ordering arrangements. The atomic structures of P2-Na2/3Ni1/3Mn2/3O2 with three different in-plane Na + -ion/vacancy orderings, (c) honeycomb type, [occ (Naf) = 0]; (d) chain type, [occ (Naf) = 1/2] and (e) large zigzag (LZZ), [occ (Naf) = 1/6]. The green ball represents the Naf site and the yellow ball stands for Nae site. (f) The atomic arrangements of Mn 4+ and Ni 2+ ions described by honeycomb ordering in the transition metal planes of P2-Na2/3Ni1/3Mn2/3O2. Supplementary Note 1. The XRD/NPD data analysis is based on crystallography. The phenomenal peaks are the direct responses to the spatial ordering arrangement of one or more species of atoms in one specific crystal structure. In terms of superstructures, they always respond with small intensities at lower diffraction angles, where they have larger lattice constants than the original structure. Hence, the high energy XRD, or NPD, is generally required to characterize these small or minor peaks.
In detail, three types of in-plane Na + -ion/vacancy orderings can be found in P2 phase according to the structural enumeration upon DFT simulations. Figure S2 shows the simulated XRD patterns of the above ordering structures using RIETAN-FP. Owing to the similar X-ray scattering factor of Ni and Mn ions, they can not be distinguished clearly. While, the small superlattice peaks in X-ray diffraction patterns can be assigned to the in-plane Na + -ion/vacancy orderings, corresponding to the d-spacings of the adjacent intralayer sodium ions. In Figure 1 of the manuscript, the clear LZZ superstructure peaks are found at 27.3° and 28.4° for P2-Na2/3Ni1/3Mn2/3O2 (inset of Figure 1a), corresponding to the d-spacings of 3.13 and 3.26 Å, respectively, which are absent in the Na2/3Ni0.3Mn0.7O2 pattern to show the structural differences. Figure S3. Simulated NPD data of P2-type layered oxides with the transition metal (TM) honeycomb ordering, the Na slab large zigzag(LZZ) ordering and the coexistence of TM honeycomb and Na LZZ ordering using GSAS II. The superstructure peaks (TM honeycomb ordering and Na slab LZZ ordering) were clearly indexed based on the provided crystal structures in table S1 with space Group of P3.

Supplementary Note 4.
Ab initio molecular dynamics (AIMD) simulations were carried out for the canonical (NVT) ensemble using a Nosé thermostat at 800 K. The cut off energy of 350 eV was setted to simulate the disordered P2-Na2/3Ni1/3Mn2/3O2 considering the current computing capabilities. The volume and the shape of the cell were fixed. The corresponding structures were heated up to the targeted temperature by the velocity scaling over 2 ps, and then equilibrated at the desired temperature. The timescale of the simulations was 10 ps and a time step of 2 fs was used to integrate the equation of motion. The overall disorder 1 [occ.
(Naf) = 1/6] and disorder 2 [occ. (Naf) = 1/12] that close to expermental results was setted to obtain two randomly arranged Na configurations. Figure S19. Na-ion diffusion in P2-Na2/3Ni1/3Mn2/3O2 of Chain type ordering (3 × 3 × 1 supercell) with monovacancy. The illustration of (a-e) Paths 1-5 in P2-Na2/3Ni1/3Mn2/3O2 atomic structure. Path1 :the migration of one Na + ions within the ab plane, where Path 1 is closer to the Mn in TM layer. (Nae-Nae) Path 2: the migration of one Na + ions within the ab plane, where Path 2 is closer to the Ni in TM layer. (Nae-Nae) Path 3: the concerted migration of two Na + ions within the ab plane, which related to the Nae-Nae-Nae. Path 4: the migration of one Na + ions within the ab plane, correspond to the Na ion migration in the chain of Naf. (Naf-Naf) Path 6: the concerted migration of two Na + ions within the ab plane, where Path 6 is closer to the Ni in TM layer. This path related to the Nae-Nae-Nae. Figure S20. Na-ion diffusion in P2-Na2/3Ni1/3Mn2/3O2 of LZZ type ordering (2[√3 × √3 × 1 ] 30°-type supercell) with monovacancy. The illustration of (a) Paths 1 and (b) 2 in P2-Na2/3Ni1/3Mn2/3O2 atomic structure. Path1 :the concerted migration of two Na + ions within the ab plane, which related to the Nae-Naf-Nae. Path 2: the concerted migration of three Na + ions within the ab plane, which related to the Nae-Naf-Nae and Nae-Nae. Figure S21. (a) Formation energies of different Na ion occupations in P3-Na2/3Ni1/3Mn2/3O2 structure, where the P3-type supercell is constructed using a 3a × 3b × 1c-type lattice with 99 atoms (Na18Ni9Mn18O54). The 3H means three layers in honeycomb ordering, the 2H+C corresponds to two layers in honeycomb and one layer in chain orderings, the1H+C stands for one layer in honeycomb and two layers in chain orderings, and the 3C is all three layers in chain ordering. The simulation results indicate the chain type ordering is energy favourable structure. (b) Crystal environments of NaO6 prism in P3 phases within the transition metal slabs. Atomic structure of P3-Na2/3Ni1/3Mn2/3O2 with the Na slab (c) honeycomb and (d) chain orderings. Figure S22. MSD of Na + ions in (a) P2-Na2/3Ni1/3Mn2/3O2 (LZZ ordering) and (b) P3-Na2/3Ni1/3Mn2/3O2 (chain ordering) as a function of time at different temperatures. Figure S23. Atomic structure of P3-Na2/3Ni1/3Mn2/3O2 with (a) Na slab honeycomb ordering and (b) chain ordering. (c) Atomic projection of the density of states of (c) P3-Na2/3Ni1/3Mn2/3O2 (three-layer honeycomb ordering) and (d) P3-Na2/3Ni1/3Mn2/3O2 (threelayer chain ordering) from which direct charge tranfer gap was indentified. Simulation show that these two different sodium ordering structures have equal band gaps. Figure S24. (a) Experimental ultra-visible light absorption spectra of P2-Na2/3Ni1/3Mn2/3O2 and P3-Na2/3Ni1/3Mn2/3O2 with the wavelength. (b) Dependence of (αhν) 2 vs. photon energy (hν), from which the optical band gap is derived, above results indicate optic band gap of P2-Na2/3Ni1/3Mn2/3O2 and P3-Na2/3Ni1/3Mn2/3O2 is equivalent roughly. Figure S25. (a) Transition metal plane with the honeycomb ordering of Mn 4+ and Ni 2+ ions in P3-Na2/3Ni1/3Mn2/3O2. (b) The Na + -ion diffusion pathway in P3-Na2/3Ni1/3Mn2/3O2 (Na slab honeycomb ordering) within the ab plane from AIMD at 800 K, and the scalebar of the isosurface is set to 0.001. (c)MSD of Na + ions in P3 Na2/3Ni1/3Mn2/3O2 (honeycomb ordering) as a function of time at different temperatures. (d) Arrhenius plot of Na + ion diffusivity in P3-Na2/3Ni1/3Mn2/3O2 (honeycomb ordering) from AIMD simulations. The error bars are the standard deviation of linear fit of MSD-Δt curves. (e) The self-part of the van Hove correlation function (Gs) for sodium in P3-Na2/3Ni1/3Mn2/3O2. (f) The distinct part of the van Hove correlation function (Gd) for sodium ions in P3-Na2/3Ni1/3Mn2/3O2. Both Gd and Gs are functions of the average Na−Na pair distance (r) and time step after thermal equilibration at 800 K.

Supplementary Note 5.
As for the stable thermodynamic configuration, from a formation energy point of view, the van Hove correlation function and probability density in P3-Na2/3Ni1/3Mn2/3O2 (chain ordering) from AIMD simulations is presented in Figure 5, and the van Hove correlation function and probability density in P3-Na2/3Ni1/3Mn2/3O2 (honeycomb ordering) from AIMD simulations is provided in Figure S25. The P3-Na2/3Ni1/3Mn2/3O2 (honeycomb ordering) exhibits a much higher activation energy of 0.31 eV. No connected channels are available within the Na slabs and the it seems difficult enough for one Na + ion diffusion to adjacent sites as shown in Figure S25 b. the peak in Gs between 0 and 2.0 Å remains unchanged after the thermal equilibration process, which implies that the Na + ions have a higher probability of staying at the initial position and are difficult to diffuse away to the neighboring sites in P3-Na2/3Ni1/3Mn2/3O2 as shown in Figure S25 e. The observed time scale of correlation (Gd) in P3-Na2/3Ni1/3Mn2/3O2 is around ~10 picoseconds at 800 K, which is much longer than that in P2-Na2/3Ni1/3Mn2/3O2 (~5 picoseconds). the van Hove correlation function indicates that Na + in P3-Na2/3Ni1/3Mn2/3O2 has a much higher probability of returning to their initial positions and staying there for a longer time duration than in P2-Na2/3Ni1/3Mn2/3O2.
Of particular importance is that much lower activation energy is observed than in P2-Na2/3Ni1/3Mn2/3O2 with respect to that in both chain and honeycomb ordering P3-Na2/3Ni1/3Mn2/3O2. Hence, the AIMD results support the conclusion fully.